One-parameter 2-equipped posets and classification of their corepresentations

TL;DR

This paper establishes a criterion for classifying corepresentations of one-parameter 2-equipped posets, providing a list of sincere cases and a matrix classification of indecomposables, linking their dimensions to roots of a quadratic form.

Contribution

It introduces a new criterion for classifying corepresentations of one-parameter 2-equipped posets and provides a comprehensive classification of indecomposables.

Findings

List of sincere one-parameter 2-equipped posets

Matrix classification of indecomposable corepresentations

Relation between dimensions and roots of the Tits quadratic form

Abstract

One-parameter criterion for 2-equipped posets with respect to cerepresentations is stated and proved. The list of sincere one-parameter 2-equipped posets is given as well as a complex matrix classification of all their indecomposables corepresentations. Relations between dimensions of indecoposable corepresentations and roots of the Tits quadratic form are also established.